Sample Solutions AP Physics B

Hecht:  Physics with Algebra/Trig

Problems

#23 f = 0.158 hz

Use T = 2p [ L / g] to calculate the period of the pendulum and then remember that f = 1/T.

T = 2p [ L / g]
T = 2p [ 10 / 9.8]
T = 2p 1.02
T = 6.35 seconds
f = 0.158 hz

#25 L = 24.8 meters

Use T = 2p [ L / g] to calculate the length of the pendulum.

T = 2p [ L / g]
10.0 = 2p [ L / 9.8]
10² = 4p² [ L / 9.8]
100(9.8)/(4p²) = L
L = 24.8 meters

#26 a = 0, b = 0.5 and c = - 0.5

An estimate might be that the period of a simple pendulum might be proportional to its mass m, length L, and the acceleration due to gravity g. Consequently, we will start with the relationship that

T = Cm^aL^bg^c

where C is a dimensionless constant.

T =		CmaLbgc
sec1		kga mb [m/sec2]c
kg0m0sec1		kga mb [mc/sec2c]
kg0m0sec1		kga mb+c sec-2c
kg:		0 = a
m:		0 = b + c b = -c b = -(-0.5) = 0.5
sec:		1 = -2c c = -0.5

T = C m⁰ L^0.5 g ^-0.5
T = C[ L / g]

#37 T₂ = 1.22 T₁

T₁ = 2p [ L / g]
T₂ = 2p [ 1.5L / g]
T₂ = 1.5  (2p [L / g] )
T₂ = 1.22  (2p [L / g] )
T₂ = 1.22 T₁